There are two key points for our parameter estimation procedure: how many room modes \(N\)  do we expect up to a given cutoff frequency \(f_c\)  and what are their approximate resonant frequencies \(\omega _n\) ?
These are dependent on the room shape and size [1]}. For a rectangular room of size \(L_x \times L_y \times L_z\)  angular eigenfrequencies are given by the expression: \(\omega _n = \pi c \sqrt{\big (\frac{n_x}{L_x}\big )^2+\big (\frac{n_y}{L_y}\big )^2+\big (\frac{n_z}{L_z}\big )^2}\)  where \((n_x, n_y, n_z) \in \mathbb {N}_0^3 \setminus (0, 0, 0)\)  and approximate number of modes up to the cutoff frequency \(f_c\)  is given by: \(\tilde{N}_{f_c} \approx \frac{4 \pi }{3} V \big (\frac{f_c}{c}\big )^3\)  where \(V=L_xL_yL_z\) .
